Multitensors as monads on categories of enriched graphs

Abstract: In this paper we unify previous developments on higher operads and multitensors into a single framework in which the interplay between multitensors on a category V, and monads on the category of graphs enriched in V, is taken as fundamental. The material presented here is the conceptual background for subsequent work in which the Gray tensor product of 2-categories and the Crans tensor product of Gray categories are exhibited as existing within our framework, and in an explicit construction of the funny tensor product of categories is generalised to a large class of Batanin operads.